The following prism is made up of 27 identical
cubes. What is the greatest possible surface area the prism
can have after removing 1 or more from the outside

The greatest possible surface area of the prism is 78 square units, it is obtained by removing center cube on each side of the prism.

Step-by-step explanation:

The given is,

                Prism is made up of 27 identical  cubes

Step:1

               Ref attachment,

               Let, surface area of one of cube = 1 square units

               Surface area of given prism,

               In the given diagram it have 9 cube sides in each side of prism.

                                  1 surface prism = 9 surface of cube

               Surface area of given prism = 6 × Surface of prism

                                                              = 6 × 9

                                                              = 54 square units          

Step:2 Check for alternative's

          For removing one cube on the edge of prism,

                      1 surface of prim = 9 surfaces of cube

          Surface area after removing cube on each side,

                                             = 6 × 11 = 66 square units

           For removing  cube on corner of prism,

                      1 surface of prim = 9 surfaces of cube

           Surface area after removing cube on corner,

                                             = 6 × 9 = 54 square units

          For removing center cube on each side,

                     1 surface of prim = 13 surfaces of cube

           Surface area after removing cube on corer on the prism,

                                                  = 6 × 13 = 78 square units

   Surface area after removing corner cube on prism = 78 square units

Result:

       The greatest possible surface area of the prism is 78 square units, it is obtained by removing center cube on each side of the prism.